The notion of a Leonard pair was introduced by the second author in [1]}.
We will recall the definition after a few comments.
A square matrix is said to be tridiagonal whenever each nonzero entry lies on
the diagonal, the subdiagonal, or the superdiagonal.
A tridiagonal matrix is said to be irreducible whenever each entry on the
subdiagonal is nonzero and each entry on the superdiagonal is nonzero.
Let \(\mathbb {F}\)  denote a field, and let \(V\)  denote a vector space over \(\mathbb {F}\) 
with finite positive dimension.
A Leonard pair on \(V\)  is an ordered pair of \(\mathbb {F}\) -linear maps \(A : V \rightarrow V\)  and
\(A^* : V \rightarrow V\) 
that satisfy (i) and (ii) below:
